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The Pseudo-wavelet Scheme for Convection Equation

Author: WangHongTao
Tutor: ShenYouJian
School: Hainan Normal University,
Course: Theory of differential equations
Keywords: Convection equation Orthogonal wavelets Multiresolution analysis Small Botailejia slightly golden methods
CLC: O174.41
Type: Master's thesis
Year: 2008
Downloads: 43
Quote: 0
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Abstract


This paper first introduces the Fourier transform and wavelet transform and some basic properties of the origin , which is mainly reflected in the first chapter , then introduced the orthogonal wavelet and scaling functions , concepts such as scale equation , which is mainly reflected in the second chapter . Mainly , for convection equation deduced time high accuracy based on orthogonal wavelet small Botailejia slightly golden (WTGM) format , and further calculations using this format numerical solution of convection , and the numerical solution obtained WGM format and exact solutions are compared in order to verify the correctness of the format . Because use of the time derivative of the Taylor series expansion , so the time accuracy is reflected in the expansion of the order in Δt , Δt higher the order , the time accuracy is better. Small Botailejia slightly golden format better use of the function field and involved operators , through this compression storage method , the matrix obtained by the operator with more zero elements, and the matrix is relatively sparse , instead of compression method , relatively dense matrix . Finally, another aspect of the application format , such as can be successfully applied in the calculation of three such combined vortex simulation, we chose the vortex interaction , primarily because the problem of nonlinear interaction strong , but this interaction is very typical two-dimensional turbulence effect.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Theory of functions > Constructive theory of functions > Approximation Theory
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